Features and References

Most of MoorDyn’s theory is described in the following publications. This page gives a very high-level overview, highlights specific theory aspects that may be important to users, and lists the papers where more detail can be found.

Features

Version 1

MoorDyn is based on a lumped-mass discretization of a mooring line’s dynamics, and adds point-mass and rigid-body objects to enable simulation of a wide variety of mooring and cabling arrangements. Hydrodynamics are included using a version of the Morison equation.

Version 2

MoorDyn v2 contains all the features of v1 with the following additional features:

• Simulation of 6 degree of freedom objects

• Non-linear tension

• Wave kinematics

• Bending stiffness

• Bathymetry

• Seabed friction

The main difference between MoorDyn-C and MoorDyn-F is that MoorDyn-C uses quaternions to describe the orientation of 6DOF objects, while F uses traditional Euler angles to handle 6DOF object rotations.

Orientation of 6 DOF objects:

MoorDyn-C, MoorDyn-F, and MoorPy share the same Intrinsic Euler-XYZ (Tait-Bryan) angles criteria to compute orientations. You can learn more about this on Hall M. Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians. Energies. 2024; 17(13):3155. https://doi.org/10.3390/en17133155

However, while on MoorDyn-F this is handled by considering orientation matrices, on MoorDyn-C quaternions are considered to describe the location and orientation of 6 DOF objects. Further description of quaternions can be found in PR #90 in the MoorDyn repository, put together by Alex Kinley of Kelson Marine: https://github.com/FloatingArrayDesign/MoorDyn/pull/90#issue-1777700494

References

The theory behind MoorDyn is available in a collection of papers, listed below by which version they were implemented in.

Version 1

The v1 lumped-mass formulation of MoorDyn as well as its validation against experiments:

M. Hall and A. Goupee, “Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data,” Ocean Engineering, vol. 104, pp. 590–603, Aug. 2015.

Coupling with WEC-Sim or any Simulink code for wave energy converter simulation:

S. Sirnivas, Y.-H. Yu, M. Hall, and B. Bosma, “Coupled Mooring Analysis for the WEC-Sim Wave Energy Converter Design Tool,” in Proceedings of the 35th International Conference on Ocean, Offshore and Arctic Engineering, Busan, South Korea, 2016.

G. Vissio, B. Passione, and M. Hall, “Expanding ISWEC Modelling with a Lumped-Mass Mooring Line Model,” presented at the European Wave and Tidal Energy Conference, Nantes, France, 2015.

Version 2

Version 2 builds upon the capabilities of Version 1. The theory behind the new features is described in the following references.

Early work on seabed friction and independent fairlead points:

M. Hall, “Efficient Modelling of Seabed Friction and Multi-Floater Mooring Systems in MoorDyn,” in Proceedings of the 12th European Wave and Tidal Energy Conference, Cork, Ireland, 2017.

Preliminary comparison of seabed friction formulations:

K. Devries, M. Hall, “Comparison of Seabed Friction Formulations in a LumpedMass Mooring Model”. in Proceedings of the ASME International Offshore Wind Technical Conference, San Francisco, California, Nov. 2018.

Overview of MoorDyn v2 (bodies, rods, and line failures):

Hall, Matthew, “MoorDyn V2: New Capabilities in Mooring System Components and Load Cases.” In Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. virtual conference, 2020.

Implementation of bending stiffness modeling for power cables:

Hall, Matthew, Senu Sirnivas, and Yi-Hsiang Yu, “Implementation and Verification of Cable Bending Stiffness in MoorDyn.” In ASME 2021 3rd International Offshore Wind Technical Conference, V001T01A011. Virtual, Online: American Society of Mechanical Engineers, 2021.

Seabed friction and bathymetry approach used in v2:

Housner, Stein, Ericka Lozon, Bruce Martin, Dorian Brefort, and Matthew Hall, “Seabed Bathymetry and Friction Modeling in MoorDyn.” Journal of Physics: Conference Series 2362, no. 1, Nov 2022: 012018.

Non-linear line stiffness:

Lozon, Ericka, Matthew Hall, Paul McEvoy, Seojin Kim, and Bradley Ling, “Design and Analysis of a Floating-Wind Shallow-Water Mooring System Featuring Polymer Springs.” American Society of Mechanical Engineers Digital Collection, 2022.

Bladed-MoorDyn Coupling:

Alexandre, Armando, Francesc Fabregas Flavia, Jingyi Yu, Ali Bakhshandehrostami, and Steven Parkinson. “Coupling Bladed With External Finite-Element Mooring Libraries.” American Society of Mechanical Engineers Digital Collection, 2023.

Viscoelastic approach for non-linear rope behavior:

Hall, Matthew, Brian Duong, and Ericka Lozon, “Streamlined Loads Analysis of Floating Wind Turbines With Fiber Rope Mooring Lines.” In ASME 2023 5th International Offshore Wind Technical Conference, V001T01A029. Exeter, UK: American Society of Mechanical Engineers, 2023.

Updated MoorDyn-OpenFOAM Coupling:

Haifei Chen, Tanausú Almeida Medina, and Jose Luis Cercos-Pita, “CFD simulation of multiple moored floating structures using OpenFOAM: An open-access mooring restraints library.” Ocean Engineering, vol. 303, Jul. 2024.

Reef3D-MoorDyn Coupling:

Soydan, Ahmet, Widar Weizhi Wang, and Hans Bihs. “An Improved Direct Forcing Immersed Boundary Method With Integrated Mooring Algorithm for Floating Offshore Wind Turbines.” American Society of Mechanical Engineers Digital Collection, 2024.

Modeling of Bi-stable Nonlinear Energy Sinks in MoorDyn (most recent description of MoorDyn theory):

Anargyros Michaloliakos, Wei-Ying Wong, Ryan Davies, Malakonda Reddy Lekkala, Matthew Hall, Lei Zuo, Alexander F. Vakakis, “Stabilizing dynamic subsea power cables using Bi-stable nonlinear energy sinks”, Ocean Engineering, vol. 334, August 2025.

Syrope model for polyester ropes:

Wei, Zhilong, Harry B. Bingham, and Yanlin Shao. 2026. “ESOMOOR D5.1: Extended Moordyn Solver and Validation Report”. Technical University of Denmark.

The Fortran version of MoorDyn is available as a module inside of OpenFAST:

https://openfast.readthedocs.io/en/main/

Hydrodynamics of 6DOF objects follows a similar approach to Hydrodyn:

https://www.nrel.gov/wind/nwtc/assets/downloads/HydroDyn/HydroDyn_Manual.pdf

Quaternion references:

1. Fossen, Thor I. Handbook of marine craft hydrodynamics and motion control. Page 25 John Wiley & Sons, 2011.

2. https://en.wikipedia.org/wiki/Gimbal_lock

3. https://www.ashwinnarayan.com/post/how-to-integrate-quaternions/

4. https://en.wikipedia.org/wiki/Quaternion#Hamilton_product

MoorDyn-C Packages used:

• Eigen: https://eigen.tuxfamily.org

• Catch2: https://github.com/catchorg/Catch2

• KISSFFT: https://github.com/mborgerding/kissfft